STEPS
Begin by making the icing: Heat 1/2 Cup milk in a saucepan with lavender flowers. Set aside, allowing flowers to steep until milk has cooled to room temperature. Put powdered sugar in a bowl. Strain flowers from the milk and pour milk into bowl with sugar. Whisk together the flavored milk and powdered sugar until icing mixture is well-blended and smooth.

Preheat the oven to 350°F. Stir the lemon zest into the granulated sugar. Whisk together the other dry ingredients: flour, salt, sugar, and baking powder in a medium sized bowl. In another bowl, beat together the “wet” ingredients: the eggs, vanilla extract, olive oil and milk, beating until mixture is smooth. Add the wet ingredients to the dry ingredients, a little at a time, stirring only just to combine.

Drop cookie dough by the tablespoonful onto a lightly oiled cookie sheet, each cookie about 2 inches apart and bake in the oven for 12 to 15 minutes, or until the edges begin to turn golden on the edges. Allow the cookies to cool on the sheet for a couple minutes before transferring to a wire wrack to cool completely.

Once cookies are cool, spread lavender icing over each one.

Store any leftover cookies in a single layer, in an airtight container, in the refrigerator for up to five days.